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Applications of Logarithms01:28

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Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
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Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log⁡(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions are...
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Related Experiment Video

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Logarithmic analog-to-digital converter using switched attenuators.

B Gottschalk1

  • 1Northeastern University, Boston, Massachusetts 02115.

The Review of Scientific Instruments
|February 1, 1978
PubMed
Summary

This study introduces a novel logarithmic analog-to-digital converter (ADC) using switched attenuators. This digital approach offers precise, relative voltage measurements across a wide range, comparable to linear ADCs in cost and speed.

Area of Science:

  • Electrical Engineering
  • Signal Processing
  • Instrumentation

Background:

  • Traditional linear analog-to-digital converters (ADCs) measure absolute voltage changes.
  • Logarithmic ADCs offer advantages for wide dynamic range measurements but often rely on device-specific characteristics.
  • Existing logarithmic converters may have limitations in accuracy or complexity.

Purpose of the Study:

  • To develop a successive-approximation analog-to-digital converter (ADC) with a logarithmic output.
  • To achieve a digital output proportional to the logarithm of the input voltage.
  • To demonstrate a digital principle for logarithmic conversion independent of solid-state device characteristics.

Main Methods:

  • Utilized independent electronically switched attenuators in a successive-approximation ADC architecture.

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  • Designed the ADC such that output step size reflects a constant relative voltage change.
  • Employed a digital approach relying on resistor accuracy rather than semiconductor properties.

    • Main Results:

    • A ten-bit prototype demonstrated adherence to an ideal logarithmic characteristic within 1% accuracy.
    • The converter effectively measured inputs across a four-decade range (1 mV to 10 V) with high precision.
    • Achieved approximately 1% measurement accuracy over the entire specified input voltage range.

    Conclusions:

    • A practical, digitally implemented logarithmic ADC is feasible using switched attenuators.
    • This design offers a robust alternative to logarithmic converters dependent on semiconductor characteristics.
    • The developed logarithmic ADC provides comparable complexity, cost, and speed to linear ADCs while offering superior dynamic range measurement.